Broadband spectrum is one which is inclusive of all the observed wavelength ranges. In the case of the BB spectra of our Sun, there is a sharp (non-differentiable) kink in the curve in the UV-range (as shown above). What is the significance of this kink?

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The point here is, that the kink you're pointing out is not belonging to the BB-spectrum of the sun.
This part of the solar spectrum is a classic example for a broad class of radiation, called nonthermal radiation.
The physical origin of this is in general that, every accelerated particle will radiate part of its energy away, with the experienced acceleration a, radiated power P and their relation $P \sim a^2$ in a wavelength-range depending on the exact process.
The origins of those accelerations are usually thought to be strong magnetic interactions on the solar surface plasma, creating the famous sunspots and coronal loops. In those loops, electrons and protons are being shot into space, following the loop, and then return back onto the solar 'surface'. Upon return they release Bremsstrahlung, as the interactions between loop-particles and surface plasma create strong braking accelerations.

Spectrae for such processes are derived in every standard textbook about theoretical astrophysics and are given by roughly $\frac{dP}{dt} \sim exp(-\frac{h \nu}{k_BT})$, which should fit the UV-part in the spectrum you gave pretty well.
This now also explains the variability of this part of the solar spectrum: As the number of loops and sunspots correlates with solar activity, it is clear that the UV-bremsstrahlung-production should too.
There is however much more to this, if you are interested. Given certain violent outbreaks that happen upon release of magnetic energy, there are modulations of the emitted radio flux (also indicated in your graph) up higher-energetic regions of x-rays.